1
a) A=1 +1/3+1/5+…..+1/97+1/99
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1/1.99+1/3.97+1/5.99+……+1/97.3+1/99.9
b) B=1/2+1/3+1/4+…..+1/99+1/100
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99/1+98/2+97/3+……+1/99
2a)CM: 2n/b(b+m)(b+2m)=1/b(b+m)-1/(b+m)(b+2m)
b)Tính tổng:S=1/1.2.3+1/2.3.4+1/3.4.5+….+1/37.38.39
nhanh lên giúp mình với
Giải thích các bước giải:
a.Ta có :
$A_m=\dfrac{1}{1.99}+\dfrac{1}{3.97}..+\dfrac{1}{97.3}+\dfrac{1}{99.1}$
$\rightarrow 100A_m=\dfrac{100}{1.99}+\dfrac{100}{3.97}..+\dfrac{100}{97.3}+\dfrac{100}{99.1}$
$\rightarrow 100A_m=\dfrac{1+99}{1.99}+\dfrac{3+97}{3.97}..+\dfrac{97+3}{97.3}+\dfrac{99+1}{99.1}$
$\rightarrow 100A_m=\dfrac{1}{1}+\dfrac{1}{99}+\dfrac{1}{3}+\dfrac{1}{97}+..+\dfrac{1}{99}+\dfrac{1}{1}$
$\rightarrow 100A_m=2(1+\dfrac{1}{3}+\dfrac{1}{5}+..+\dfrac{1}{99})$
$\rightarrow A_m=\dfrac{1}{50}(1+\dfrac{1}{3}+\dfrac{1}{5}+..+\dfrac{1}{99})$
$\rightarrow A=\dfrac{1+\dfrac{1}{3}+\dfrac{1}{5}+..+\dfrac{1}{99}}{A_m}=50$